Anisotropic modeling of structural components using embedded crystal plasticity constructive laws within finite elements

Abstract

a b s t r a c tPins are commonly used to join members of mechanical mechanisms. In order to maintain the integrity of the joint and prevent failure, there must be sufficient material of adequate strength around the pin hole to sustain the bearing and tear out loads from the pin connection. In this work, a multi-scale materials simulation model based on finite elements (FE) is developed for design and evaluation of materials for such applications. We specifically examine several constitutive models for simulating the elasto-plastic behavior of the plate material while maintaining computational efficiency. Here, models are developed for two plate materials: copper (Cu) and α-uranium (α-U), with vastly different plastic behaviors owing to their crystal structures and crystallographic textures. For Cu, digital image correlation (DIC) tests are carried out during loading of the plate/pin assembly to characterize the strain distributions in the critical hole/pin area. The corresponding FE simulations are carried out using a combination of constitutive laws involving a fine-scale polycrystal plasticity calculation, a J2 flow theory, or a combination of both. We show that the FE model using the fine-scale polycrystal plasticity constitutive law successfully captures the DIC strain fields in the hole region at different plate displacements. Surprisingly, use of the more computationally efficient J2 plasticity model also produces reasonable results in comparison with the measurements and the fine-scale constitutive law. An interesting finding is that combining fine-scale constitutive laws in the region surrounding the hole and continuum J2 theory elsewhere gives the worst agreement. It also precariously produces non-conservative estimates for the hole opening with applied displacement. These results on Cu helped subsequent simulations on α-U, where use of the fine-scale polycrystal simulation is fundamental considering the highly plastic anisotropic response of this complicated material. We demonstrate that in the α-U plates, the localized deformation in the hole region is highly dependent on the direction of displacement.

Multiscale Modeling of Microstructure‐Property Relationships of Polycrystalline Metals during Thermo‐Mechanical Deformation

“…Metals, such as Ta, Nb and ferritic steel, with a body‐centered cubic (BCC) crystal structure, have two or three families, making up 24 or 48 slip systems . Metals with hexagonal close packed (HCP) crystal structure like Mg, Zr, Be, or Ti metals as well as orthorhombic crystal structure like U, possess an even larger suite of slip families and systems . Moreover these low symmetry crystal structure metals deform by multiple variant of twins .…”

A numerical procedure enabling accurate descriptions of strain rate-sensitive flow of polycrystals within crystal visco-plasticity theory

“…Most pure metals with a face centered cubic crystal structure (e.g., Cu, Ni, Al) deform on one slip family 111 〈11 0〉, which contains twelve independently oriented slip systems [12][13][14].Metals, such as steel and most of refractory metals, with a body-centered cubic crystal structure, have two or three families, making up 24 or 48 slip systems [15][16][17][18][19]. Metals with a lower symmetry crystal structure, like hexagonal close packed Mg, Zr, Be, or Ti metals or orthorhombic U, possess an even larger suite of slip families and systems [20][21][22][23][24][25]. When plastically deformed, a crystal accommodates strain using a small subset of these systems.Which systems are activated, how many, and the distribution of shear among them are collectively referred to as slip activity.…”

Texture formation in orthorhombic alpha-uranium under simple compression and rolling to high strains

“…It is generally found that the multiple slip and twinning modes are active within individual crystals of a-U and such complex combinations are needed to explain its strong plastic anisotropy in macroscopic behavior [2,16,17]. Further, the slip modes differ in their sensitivity to temperature and strain rate leading to interesting and substantial changes in the constitutive response as temperature or strain rate changes [18].…”